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          <h1 class="post-title" itemprop="name headline">编程之美将帅不照面</h1>
        

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        <p>编程之美上的一道题：要求将帅不能照面，找到有多少种方式摆放“将”和“帅”，而且只能使用一个变量。</p>
<p>思考：如果蛮力法解决，只需要罗列出所有的可能性，然后排除掉那些不满足条件的情况就是结果了。但是，这里只能用一个变量保存结果，所以，需要一点技巧，先说一下《编程之美》是的解法2,因为解法2是最精妙的，个人认为，提供了一种新型的思考方式。先给出将帅在棋局的分布，有一个感观的认识再继续下面的操作：</p>
<p><img src="/2020/07/20/%E7%BC%96%E7%A8%8B%E4%B9%8B%E7%BE%8E%E5%B0%86%E5%B8%85%E4%B8%8D%E7%85%A7%E9%9D%A2/SouthEast" alt="img"></p>
<p>解法二：我们可以这么做，下面的二维特殊数k{1,2,3,4,5,….9},其中k=1,2,3,4,…..9.表示A中的k和B中的1,2,…9搭配成一对，这样子的话就可以搭配出9*9=81种可能性.理论上，我们只需要遍历完这81种情况就可以找到结果。A格子和B格子的棋子只有在同一列才会产生冲突。那么重点就是如何找到列数。</p>
<p>先列举出所以的可能性组合：</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line">１&#123;1,1&#125;&#123;1,2&#125;&#123;1,3&#125;&#123;1,4&#125;&#123;1,5&#125;&#123;1,6&#125;&#123;1,7&#125;&#123;1,8&#125;&#123;1,9&#125;</span><br><span class="line">２&#123;2,1&#125;&#123;2,2&#125;&#123;2,3&#125;&#123;2,4&#125;&#123;2,5&#125;&#123;2,6&#125;&#123;2,7&#125;&#123;2,8&#125;&#123;2,9&#125;</span><br><span class="line">３&#123;3,1&#125;&#123;3,2&#125;&#123;3,3&#125;&#123;3,4&#125;&#123;3,5&#125;&#123;3,6&#125;&#123;3,7&#125;&#123;3,8&#125;&#123;3,9&#125;</span><br><span class="line">４&#123;4,1&#125;&#123;4,2&#125;&#123;4,3&#125;&#123;4,4&#125;&#123;4,5&#125;&#123;4,6&#125;&#123;4,7&#125;&#123;4,8&#125;&#123;4,9&#125;</span><br><span class="line">５&#123;5,1&#125;&#123;5,2&#125;&#123;5,3&#125;&#123;5,4&#125;&#123;5,5&#125;&#123;5,6&#125;&#123;5,7&#125;&#123;5,8&#125;&#123;5,9&#125;</span><br><span class="line">６&#123;6,1&#125;&#123;6,2&#125;&#123;6,3&#125;&#123;6,4&#125;&#123;6,5&#125;&#123;6,6&#125;&#123;6,7&#125;&#123;6,8&#125;&#123;6,9&#125;</span><br><span class="line">７&#123;7,1&#125;&#123;7,2&#125;&#123;7,3&#125;&#123;7,4&#125;&#123;7,5&#125;&#123;7,6&#125;&#123;7,7&#125;&#123;7,8&#125;&#123;7,9&#125;</span><br><span class="line">８&#123;8,1&#125;&#123;8,2&#125;&#123;8,3&#125;&#123;8,4&#125;&#123;8,5&#125;&#123;8,6&#125;&#123;8,7&#125;&#123;8,8&#125;&#123;8,9&#125;</span><br><span class="line">９&#123;9,1&#125;&#123;9,2&#125;&#123;9,3&#125;&#123;9,4&#125;&#123;9,5&#125;&#123;9,6&#125;&#123;9,7&#125;&#123;9,8&#125;&#123;9,9&#125;</span><br></pre></td></tr></table></figure>

<p>第1行就是A中第1格和B中的九格对应的情况，其它类比如是</p>
<p>像<code>for(i=1;i&lt;=81;++i)</code>中的<code>i</code>,</p>
<p>如果我们想确定它是A中的第几格，怎么办？可以对i除以9，就知道它是第几行，即A中第几格，如果还想知道它在A中第几列，继续对它模3即可。</p>
<p>现在开始考虑B中的情况，如何知道当前i是B中的第几格？这个问题可以转化成如何知道它是上面二维数组中第几列，只需要对i模上9即可，那么如何知道它是B中的第几列呢？继续对它模上3即可。</p>
<p>小结拓展：</p>
<p>我们知道A[i][j]实质上表示的是A数组中(i*cols+j)号元素，那么，如果我们知道元素是第k号元素了，要如何确定它的行号和列号呢？<code>row=k/cols,col=k%cols</code>.再把这个基本思路套到上面应该能够找到一点灵感了。</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line">#include&lt;stdio.h&gt;</span><br><span class="line">int main()</span><br><span class="line">&#123;</span><br><span class="line">	int i&#x3D;81;</span><br><span class="line">	while(i--)</span><br><span class="line">	&#123;</span><br><span class="line">		if( i&#x2F;9%3 &#x3D;&#x3D; i%9%3)&#x2F;&#x2F;i&#x2F;9求的是行号(A中号码)，i%9求的是列号(B中号码)</span><br><span class="line">			continue;</span><br><span class="line">		printf(&quot;%d %d\n&quot;,i&#x2F;9+1,i%9+1);&#x2F;&#x2F;输出A,B中的号码</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>


<p>总结：<br>可以将A中的9个格子{1,2,3,4,5,6,7,8,9}当成行号，将B中的9个格子{1,2,3,4,5,6,7,8,9}当成列号，那么就可以组成一个A[i][j]二维数组，只不过题目要求我们只能使用一个变量，否则我们只需要保存两个变量i,j，遍历完整个数组就可以了。但是，我们也可以用一维数组的方式存储二维数组的下标，假定一维数组的下标是k,则i=k/cols,j=k%cols.</p>
<p>这让我想到这篇博文的35和36行。<a href="http://blog.csdn.net/linraise/article/details/12571025" target="_blank" rel="noopener">http://blog.csdn.net/linraise/article/details/12571025</a></p>
<p>剩下的就可以完全按照二维数组的形式解决这个问题了。</p>
<p>解法三：用一个结构体保存两个变量，实质上和直接使用二维下标的思路一样。这里不再多说。</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line">int main()</span><br><span class="line">&#123;</span><br><span class="line">	struct </span><br><span class="line">	&#123;</span><br><span class="line">		unsigned char a:4;</span><br><span class="line">		unsigned char b:4;</span><br><span class="line">	&#125; i;</span><br><span class="line">	for(i.a&#x3D;1;i.a&lt;&#x3D;9;++i.a)</span><br><span class="line">	&#123;</span><br><span class="line">		for(i.b&#x3D;1;i.b&lt;&#x3D;9;++i.b)</span><br><span class="line">		&#123;</span><br><span class="line">			if( i.a % 3 !&#x3D; i.b % 3)</span><br><span class="line">				printf(&quot;A &#x3D; %d, B &#x3D; %d\n&quot;,i.a,i.b);</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>




      
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  <script type="text/javascript">
    // Popup Window;
    var isfetched = false;
    var isXml = true;
    // Search DB path;
    var search_path = "search.xml";
    if (search_path.length === 0) {
      search_path = "search.xml";
    } else if (/json$/i.test(search_path)) {
      isXml = false;
    }
    var path = "/" + search_path;
    // monitor main search box;

    var onPopupClose = function (e) {
      $('.popup').hide();
      $('#local-search-input').val('');
      $('.search-result-list').remove();
      $('#no-result').remove();
      $(".local-search-pop-overlay").remove();
      $('body').css('overflow', '');
    }

    function proceedsearch() {
      $("body")
        .append('<div class="search-popup-overlay local-search-pop-overlay"></div>')
        .css('overflow', 'hidden');
      $('.search-popup-overlay').click(onPopupClose);
      $('.popup').toggle();
      var $localSearchInput = $('#local-search-input');
      $localSearchInput.attr("autocapitalize", "none");
      $localSearchInput.attr("autocorrect", "off");
      $localSearchInput.focus();
    }

    // search function;
    var searchFunc = function(path, search_id, content_id) {
      'use strict';

      // start loading animation
      $("body")
        .append('<div class="search-popup-overlay local-search-pop-overlay">' +
          '<div id="search-loading-icon">' +
          '<i class="fa fa-spinner fa-pulse fa-5x fa-fw"></i>' +
          '</div>' +
          '</div>')
        .css('overflow', 'hidden');
      $("#search-loading-icon").css('margin', '20% auto 0 auto').css('text-align', 'center');

      $.ajax({
        url: path,
        dataType: isXml ? "xml" : "json",
        async: true,
        success: function(res) {
          // get the contents from search data
          isfetched = true;
          $('.popup').detach().appendTo('.header-inner');
          var datas = isXml ? $("entry", res).map(function() {
            return {
              title: $("title", this).text(),
              content: $("content",this).text(),
              url: $("url" , this).text()
            };
          }).get() : res;
          var input = document.getElementById(search_id);
          var resultContent = document.getElementById(content_id);
          var inputEventFunction = function() {
            var searchText = input.value.trim().toLowerCase();
            var keywords = searchText.split(/[\s\-]+/);
            if (keywords.length > 1) {
              keywords.push(searchText);
            }
            var resultItems = [];
            if (searchText.length > 0) {
              // perform local searching
              datas.forEach(function(data) {
                var isMatch = false;
                var hitCount = 0;
                var searchTextCount = 0;
                var title = data.title.trim();
                var titleInLowerCase = title.toLowerCase();
                var content = data.content.trim().replace(/<[^>]+>/g,"");
                var contentInLowerCase = content.toLowerCase();
                var articleUrl = decodeURIComponent(data.url);
                var indexOfTitle = [];
                var indexOfContent = [];
                // only match articles with not empty titles
                if(title != '') {
                  keywords.forEach(function(keyword) {
                    function getIndexByWord(word, text, caseSensitive) {
                      var wordLen = word.length;
                      if (wordLen === 0) {
                        return [];
                      }
                      var startPosition = 0, position = [], index = [];
                      if (!caseSensitive) {
                        text = text.toLowerCase();
                        word = word.toLowerCase();
                      }
                      while ((position = text.indexOf(word, startPosition)) > -1) {
                        index.push({position: position, word: word});
                        startPosition = position + wordLen;
                      }
                      return index;
                    }

                    indexOfTitle = indexOfTitle.concat(getIndexByWord(keyword, titleInLowerCase, false));
                    indexOfContent = indexOfContent.concat(getIndexByWord(keyword, contentInLowerCase, false));
                  });
                  if (indexOfTitle.length > 0 || indexOfContent.length > 0) {
                    isMatch = true;
                    hitCount = indexOfTitle.length + indexOfContent.length;
                  }
                }

                // show search results

                if (isMatch) {
                  // sort index by position of keyword

                  [indexOfTitle, indexOfContent].forEach(function (index) {
                    index.sort(function (itemLeft, itemRight) {
                      if (itemRight.position !== itemLeft.position) {
                        return itemRight.position - itemLeft.position;
                      } else {
                        return itemLeft.word.length - itemRight.word.length;
                      }
                    });
                  });

                  // merge hits into slices

                  function mergeIntoSlice(text, start, end, index) {
                    var item = index[index.length - 1];
                    var position = item.position;
                    var word = item.word;
                    var hits = [];
                    var searchTextCountInSlice = 0;
                    while (position + word.length <= end && index.length != 0) {
                      if (word === searchText) {
                        searchTextCountInSlice++;
                      }
                      hits.push({position: position, length: word.length});
                      var wordEnd = position + word.length;

                      // move to next position of hit

                      index.pop();
                      while (index.length != 0) {
                        item = index[index.length - 1];
                        position = item.position;
                        word = item.word;
                        if (wordEnd > position) {
                          index.pop();
                        } else {
                          break;
                        }
                      }
                    }
                    searchTextCount += searchTextCountInSlice;
                    return {
                      hits: hits,
                      start: start,
                      end: end,
                      searchTextCount: searchTextCountInSlice
                    };
                  }

                  var slicesOfTitle = [];
                  if (indexOfTitle.length != 0) {
                    slicesOfTitle.push(mergeIntoSlice(title, 0, title.length, indexOfTitle));
                  }

                  var slicesOfContent = [];
                  while (indexOfContent.length != 0) {
                    var item = indexOfContent[indexOfContent.length - 1];
                    var position = item.position;
                    var word = item.word;
                    // cut out 100 characters
                    var start = position - 20;
                    var end = position + 80;
                    if(start < 0){
                      start = 0;
                    }
                    if (end < position + word.length) {
                      end = position + word.length;
                    }
                    if(end > content.length){
                      end = content.length;
                    }
                    slicesOfContent.push(mergeIntoSlice(content, start, end, indexOfContent));
                  }

                  // sort slices in content by search text's count and hits' count

                  slicesOfContent.sort(function (sliceLeft, sliceRight) {
                    if (sliceLeft.searchTextCount !== sliceRight.searchTextCount) {
                      return sliceRight.searchTextCount - sliceLeft.searchTextCount;
                    } else if (sliceLeft.hits.length !== sliceRight.hits.length) {
                      return sliceRight.hits.length - sliceLeft.hits.length;
                    } else {
                      return sliceLeft.start - sliceRight.start;
                    }
                  });

                  // select top N slices in content

                  var upperBound = parseInt('1');
                  if (upperBound >= 0) {
                    slicesOfContent = slicesOfContent.slice(0, upperBound);
                  }

                  // highlight title and content

                  function highlightKeyword(text, slice) {
                    var result = '';
                    var prevEnd = slice.start;
                    slice.hits.forEach(function (hit) {
                      result += text.substring(prevEnd, hit.position);
                      var end = hit.position + hit.length;
                      result += '<b class="search-keyword">' + text.substring(hit.position, end) + '</b>';
                      prevEnd = end;
                    });
                    result += text.substring(prevEnd, slice.end);
                    return result;
                  }

                  var resultItem = '';

                  if (slicesOfTitle.length != 0) {
                    resultItem += "<li><a href='" + articleUrl + "' class='search-result-title'>" + highlightKeyword(title, slicesOfTitle[0]) + "</a>";
                  } else {
                    resultItem += "<li><a href='" + articleUrl + "' class='search-result-title'>" + title + "</a>";
                  }

                  slicesOfContent.forEach(function (slice) {
                    resultItem += "<a href='" + articleUrl + "'>" +
                      "<p class=\"search-result\">" + highlightKeyword(content, slice) +
                      "...</p>" + "</a>";
                  });

                  resultItem += "</li>";
                  resultItems.push({
                    item: resultItem,
                    searchTextCount: searchTextCount,
                    hitCount: hitCount,
                    id: resultItems.length
                  });
                }
              })
            };
            if (keywords.length === 1 && keywords[0] === "") {
              resultContent.innerHTML = '<div id="no-result"><i class="fa fa-search fa-5x" /></div>'
            } else if (resultItems.length === 0) {
              resultContent.innerHTML = '<div id="no-result"><i class="fa fa-frown-o fa-5x" /></div>'
            } else {
              resultItems.sort(function (resultLeft, resultRight) {
                if (resultLeft.searchTextCount !== resultRight.searchTextCount) {
                  return resultRight.searchTextCount - resultLeft.searchTextCount;
                } else if (resultLeft.hitCount !== resultRight.hitCount) {
                  return resultRight.hitCount - resultLeft.hitCount;
                } else {
                  return resultRight.id - resultLeft.id;
                }
              });
              var searchResultList = '<ul class=\"search-result-list\">';
              resultItems.forEach(function (result) {
                searchResultList += result.item;
              })
              searchResultList += "</ul>";
              resultContent.innerHTML = searchResultList;
            }
          }

          if ('auto' === 'auto') {
            input.addEventListener('input', inputEventFunction);
          } else {
            $('.search-icon').click(inputEventFunction);
            input.addEventListener('keypress', function (event) {
              if (event.keyCode === 13) {
                inputEventFunction();
              }
            });
          }

          // remove loading animation
          $(".local-search-pop-overlay").remove();
          $('body').css('overflow', '');

          proceedsearch();
        }
      });
    }

    // handle and trigger popup window;
    $('.popup-trigger').click(function(e) {
      e.stopPropagation();
      if (isfetched === false) {
        searchFunc(path, 'local-search-input', 'local-search-result');
      } else {
        proceedsearch();
      };
    });

    $('.popup-btn-close').click(onPopupClose);
    $('.popup').click(function(e){
      e.stopPropagation();
    });
    $(document).on('keyup', function (event) {
      var shouldDismissSearchPopup = event.which === 27 &&
        $('.search-popup').is(':visible');
      if (shouldDismissSearchPopup) {
        onPopupClose();
      }
    });
  </script>





  

  

  

  
  

  

  

  

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</html>
